Fibrés principaux sur les corps valués henséliens

DOI10.14231/AG-2014-025zbMATH Open1322.14068arXiv1309.6430OpenAlexW2319518064MaRDI QIDQ3192616

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Publication date: 13 October 2015

Published in: (Search for Journal in Brave)

Abstract: Let (K,v) be a valued field, Y a K-variety, G an algebraic group over K (not necessarily smooth), and f: X->Y a G-torsor over Y. We consider the induced map X(K)-->Y(K), which is continuous for the topologies deduced from the valuation. Let I denote the image of this map. We prove that if (K,v) is henselian and its completion is a separable extension, then: - I is locally closed in Y(K); - the induced surjection X(K)-->I is a principal bundle with group G(K) (also topologized by the valuation).

Full work available at URL: https://arxiv.org/abs/1309.6430

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